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Simplifying (2 + z)(4z + 3) = 0 Reorder the terms: (2 + z)(3 + 4z) = 0 Multiply (2 + z) * (3 + 4z) (2(3 + 4z) + z(3 + 4z)) = 0 ((3 * 2 + 4z * 2) + z(3 + 4z)) = 0 ((6 + 8z) + z(3 + 4z)) = 0 (6 + 8z + (3 * z + 4z * z)) = 0 (6 + 8z + (3z + 4z2)) = 0 Combine like terms: 8z + 3z = 11z (6 + 11z + 4z2) = 0 Solving 6 + 11z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + z)(3 + 4z) = 0Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve: Simplifying 3 + 4z = 0 Solving 3 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4z = 0 + -3 4z = 0 + -3 Combine like terms: 0 + -3 = -3 4z = -3 Divide each side by '4'. z = -0.75 Simplifying z = -0.75Solution
z = {-2, -0.75}
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